I'll chime in on this part... The obvious option for one-stop and one award would be YYZ-DFW-ICN all on AA. You could also do YYZ-HKG-ICN on CX, but that would price as two awards (and so cost a few more miles) as you cannot transit Asia 2 on a North America-Asia 1 award. I certainly stand to be corrected, but I think those are your only options to keep it down to 1 stop.

With 2 stops you've got access to NRT via LAX, JFK, ORD and DFW since AA fly to all four cities from YYZ, and as you note JL do serve ICN from NRT. Hawaiian Airlines also serve ICN from HNL, but I'm not sure how frequently or whether it's even feasible to find award space on that flight–I'd stick to the other options, but did want to throw this out in case you want to try and work in a 23 hour stop in the sun.